O teorema central do limite: um estudo ecológico do saber e do didático
Autor(a) principal: | |
---|---|
Data de Publicação: | 2009 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://tede2.pucsp.br/handle/handle/11426 |
Resumo: | This paper refers to the building of mathematical and/or statistical ideas and concepts around Central Limit Theorem for Mathematics graduates.The investigation focuses the importance of the theorem in Statistics Inference and its comprehension by the professionals to be, who will act in Basic Education. Therefore, we chose to research some books related to the teaching and learning process of the theorem and emphasised its importance on the Mathematics teacher daily practice. The theoretical approach is about Mathematics Teaching theories, particularly the Theory of Didactic Transposition ( CHEVALLARD, 1985), with an echological approach under the knowlwdge and teaching point of view ( ARTAUD, 1998). We chose methodological procedures directed to the didactic design (ARTIGUE, 2009), with qualitative nature, and whose assumptions are linked to Teaching Engineering (ARTIGUE, 1988). The subjects of this investigation are the graduates who had some knowledge about Basic Statistics and, from a previous analysis about the kind of knowledge they had about the theme, we presented some activities in a problem-situation context connected to the Mathematics teachers daily practice. The analysis of these results allowed us to relate the existing problems between the subject and the students from Basic Education, which involved statistics literacy. After these activities, there was a dialogue, with discussions about the theme, allowing us to analyse how the ideas and concepts around the Central Limit Theorem were built, being its comprehension the main aim for the graduates. Besides that, we analysed some textbooks for higher education, based on the Anthropological Theory of Didactic (CHEVALLARD, 1996, 1999), which also showed us the essential knowledge for the theorem to live , because the approach is under the knowledge and teaching echological point of view. On the other hand, we detected what kind of limitations, or restrictions, exist in the books analysed, interfering in the elaboration of the activities by the teacher. Thus, our investigation reaffirms the importance of teaching and learning Statistics in the various applications for the Mathematics teachers to be formation in a world controlled by the technological advances, which interfere directly on the understanding of the information we receive every moment |
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Coutinho, Cileda de Queiroz e Silvahttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4739544D6Rodrigues, Chang Kuo2016-04-27T16:59:00Z2010-01-222009-12-02Rodrigues, Chang Kuo. O teorema central do limite: um estudo ecológico do saber e do didático. 2009. 214 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2009.https://tede2.pucsp.br/handle/handle/11426This paper refers to the building of mathematical and/or statistical ideas and concepts around Central Limit Theorem for Mathematics graduates.The investigation focuses the importance of the theorem in Statistics Inference and its comprehension by the professionals to be, who will act in Basic Education. Therefore, we chose to research some books related to the teaching and learning process of the theorem and emphasised its importance on the Mathematics teacher daily practice. The theoretical approach is about Mathematics Teaching theories, particularly the Theory of Didactic Transposition ( CHEVALLARD, 1985), with an echological approach under the knowlwdge and teaching point of view ( ARTAUD, 1998). We chose methodological procedures directed to the didactic design (ARTIGUE, 2009), with qualitative nature, and whose assumptions are linked to Teaching Engineering (ARTIGUE, 1988). The subjects of this investigation are the graduates who had some knowledge about Basic Statistics and, from a previous analysis about the kind of knowledge they had about the theme, we presented some activities in a problem-situation context connected to the Mathematics teachers daily practice. The analysis of these results allowed us to relate the existing problems between the subject and the students from Basic Education, which involved statistics literacy. After these activities, there was a dialogue, with discussions about the theme, allowing us to analyse how the ideas and concepts around the Central Limit Theorem were built, being its comprehension the main aim for the graduates. Besides that, we analysed some textbooks for higher education, based on the Anthropological Theory of Didactic (CHEVALLARD, 1996, 1999), which also showed us the essential knowledge for the theorem to live , because the approach is under the knowledge and teaching echological point of view. On the other hand, we detected what kind of limitations, or restrictions, exist in the books analysed, interfering in the elaboration of the activities by the teacher. Thus, our investigation reaffirms the importance of teaching and learning Statistics in the various applications for the Mathematics teachers to be formation in a world controlled by the technological advances, which interfere directly on the understanding of the information we receive every momentO presente trabalho refere-se à construção das ideias e dos conceitos matemáticos e/ou estatísticos em torno do Teorema Central do Limite para os Licenciandos de Matemática. O cerne da investigação limita-se à importância do teorema na Inferência Estatística e à sua compreensão pelos futuros profissionais que atuarão na Educação Básica. Nesse sentido, optamos por revisar algumas bibliografias que têm relação com o processo de ensino e de aprendizagem do teorema e enfatizamos sua importância na pratica do dia a dia do professor de Matemática. O quadro teórico incide sobre as teorias da Didática da Matemática, particularmente, a Teoria da Transposição Didática (CHEVALLARD, 1985), munido de uma abordagem ecológica sob o ponto de vista do saber e do didático (ARTAUD, 1998). Optamos por procedimentos metodológicos voltados para o design didático (ARTIGUE, 2009), de cunho qualitativo e, cujos pressupostos estão aliados à Engenharia Didática (ARTIGUE, 1988). Os sujeitos dessa investigação são os licenciandos que já predispunham de conhecimentos sobre a Estatística Básica e, a partir de uma análise prévia sobre que tipos de conhecimento eles já detinham sobre o tema, apresentamos algumas atividades no contexto de uma situação-problema pertinente ao cotidiano dos professores de Matemática. A análise desses resultados nos propiciou interrelacionar as problemáticas existentes na disciplina de Matemática com alunos da Educação Básica, envolvendo assim, a literacia estatística. Após a realização dessas atividades, ocorreu também um diálogo, com discussões acerca do tema, o que nos permitiu analisar como foram construídos as ideias e os conceitos no entorno do Teorema Central do Limite, de modo que sua compreensão fosse o principal alvo para os licenciandos. Além disso, analisamos alguns livrostexto do ensino superior, à luz da Teoria Antropológica do Didático (CHEVALLARD, 1996, 1999), o que também nos indicou que saberes são indispensáveis de modo que o teorema viva , já que a abordagem é sob o ponto de vista ecológico do saber e do didático. Por outro lado, detectamos que tipos de limitações, ou restrições, existem nas obras consultadas, interferindo assim, a elaboração das atividades por parte do professor. Portanto, a nossa investigação reitera a importância do ensino e da aprendizagem da Estatística nas diversas aplicações na formação dos futuros professores de Matemática num mundo ditado pelos avanços tecnológicos, que interferem diretamente na leitura de informações que recebemos a todo instanteapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/23828/Chang%20Kuo%20Rodrigues.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBREducaçãoTeorema central do limiteEnsino de estatísticaInferência estatísticaEstatistica -- Estudo e ensinoMatematica -- Estudo e ensinoCentral limit theoremStatistics teachingStatistics inferenceCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO teorema central do limite: um estudo ecológico do saber e do didáticoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da PUC_SPinstname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPTEXTChang Kuo Rodrigues.pdf.txtChang Kuo Rodrigues.pdf.txtExtracted texttext/plain339221https://repositorio.pucsp.br/xmlui/bitstream/handle/11426/3/Chang%20Kuo%20Rodrigues.pdf.txt2974c445940fa385c760276f02cacff2MD53ORIGINALChang Kuo Rodrigues.pdfapplication/pdf19165521https://repositorio.pucsp.br/xmlui/bitstream/handle/11426/1/Chang%20Kuo%20Rodrigues.pdf423ed2c3982a3973f316dec156e2d596MD51THUMBNAILChang Kuo Rodrigues.pdf.jpgChang Kuo Rodrigues.pdf.jpgGenerated Thumbnailimage/jpeg3543https://repositorio.pucsp.br/xmlui/bitstream/handle/11426/2/Chang%20Kuo%20Rodrigues.pdf.jpg73b0ea12da66254127801ec8862cb46aMD52handle/114262022-04-27 12:47:24.083oai:repositorio.pucsp.br:handle/11426Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2022-04-27T15:47:24Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.por.fl_str_mv |
O teorema central do limite: um estudo ecológico do saber e do didático |
title |
O teorema central do limite: um estudo ecológico do saber e do didático |
spellingShingle |
O teorema central do limite: um estudo ecológico do saber e do didático Rodrigues, Chang Kuo Teorema central do limite Ensino de estatística Inferência estatística Estatistica -- Estudo e ensino Matematica -- Estudo e ensino Central limit theorem Statistics teaching Statistics inference CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O teorema central do limite: um estudo ecológico do saber e do didático |
title_full |
O teorema central do limite: um estudo ecológico do saber e do didático |
title_fullStr |
O teorema central do limite: um estudo ecológico do saber e do didático |
title_full_unstemmed |
O teorema central do limite: um estudo ecológico do saber e do didático |
title_sort |
O teorema central do limite: um estudo ecológico do saber e do didático |
author |
Rodrigues, Chang Kuo |
author_facet |
Rodrigues, Chang Kuo |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Coutinho, Cileda de Queiroz e Silva |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4739544D6 |
dc.contributor.author.fl_str_mv |
Rodrigues, Chang Kuo |
contributor_str_mv |
Coutinho, Cileda de Queiroz e Silva |
dc.subject.por.fl_str_mv |
Teorema central do limite Ensino de estatística Inferência estatística Estatistica -- Estudo e ensino Matematica -- Estudo e ensino |
topic |
Teorema central do limite Ensino de estatística Inferência estatística Estatistica -- Estudo e ensino Matematica -- Estudo e ensino Central limit theorem Statistics teaching Statistics inference CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Central limit theorem Statistics teaching Statistics inference |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This paper refers to the building of mathematical and/or statistical ideas and concepts around Central Limit Theorem for Mathematics graduates.The investigation focuses the importance of the theorem in Statistics Inference and its comprehension by the professionals to be, who will act in Basic Education. Therefore, we chose to research some books related to the teaching and learning process of the theorem and emphasised its importance on the Mathematics teacher daily practice. The theoretical approach is about Mathematics Teaching theories, particularly the Theory of Didactic Transposition ( CHEVALLARD, 1985), with an echological approach under the knowlwdge and teaching point of view ( ARTAUD, 1998). We chose methodological procedures directed to the didactic design (ARTIGUE, 2009), with qualitative nature, and whose assumptions are linked to Teaching Engineering (ARTIGUE, 1988). The subjects of this investigation are the graduates who had some knowledge about Basic Statistics and, from a previous analysis about the kind of knowledge they had about the theme, we presented some activities in a problem-situation context connected to the Mathematics teachers daily practice. The analysis of these results allowed us to relate the existing problems between the subject and the students from Basic Education, which involved statistics literacy. After these activities, there was a dialogue, with discussions about the theme, allowing us to analyse how the ideas and concepts around the Central Limit Theorem were built, being its comprehension the main aim for the graduates. Besides that, we analysed some textbooks for higher education, based on the Anthropological Theory of Didactic (CHEVALLARD, 1996, 1999), which also showed us the essential knowledge for the theorem to live , because the approach is under the knowledge and teaching echological point of view. On the other hand, we detected what kind of limitations, or restrictions, exist in the books analysed, interfering in the elaboration of the activities by the teacher. Thus, our investigation reaffirms the importance of teaching and learning Statistics in the various applications for the Mathematics teachers to be formation in a world controlled by the technological advances, which interfere directly on the understanding of the information we receive every moment |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009-12-02 |
dc.date.available.fl_str_mv |
2010-01-22 |
dc.date.accessioned.fl_str_mv |
2016-04-27T16:59:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Rodrigues, Chang Kuo. O teorema central do limite: um estudo ecológico do saber e do didático. 2009. 214 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2009. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/11426 |
identifier_str_mv |
Rodrigues, Chang Kuo. O teorema central do limite: um estudo ecológico do saber e do didático. 2009. 214 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2009. |
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https://tede2.pucsp.br/handle/handle/11426 |
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por |
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Pontifícia Universidade Católica de São Paulo |
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Programa de Estudos Pós-Graduados em Educação Matemática |
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PUC-SP |
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BR |
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Pontifícia Universidade Católica de São Paulo |
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